Theorem simp3i 1141

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  hartogslem2  9435  harwdom  9483  divalglem6  16309  structfn  17067  strleun  17068  oppchomfval  17620  sratset  21087  srads  21089  tngip  24533  dfrelog  26472  log2ub  26857  birthdaylem3  26861  birthday  26862  divsqrtsum2  26891  harmonicbnd2  26913  lgslem4  27209  lgscllem  27213  lgsdir2lem2  27235  lgsdir2lem3  27236  mulog2sumlem1  27443  siilem2  30796  h2hva  30918  h2hsm  30919  h2hnm  30920  elunop2  31957  wallispilem3  46048  wallispilem4  46049  prstchomval  49544  cnelsubclem  49588